Tune learned from the late Billy Harrison. Billy referred to it as his dads carol. In the early part of the 20th century Billy, his father and one or two others played their carols in and around the villages of Nunburnholme and Millington. They are villages at the western escarpment of the Yorkshire Wolds.
As an old man Billy taught his tunes to the young Jim Eldon. Because Billy knew seconds to many of his melodies, he was keen to teach and share them. That way he had a lead line along with which to play his seconds.
Billy told Jim that he didn't know any words to it.
Because Billy had several strong tunes to 'While Shepherds', and because the 'While Shepherds' verses are drawn directly from the St. Luke gospel, in writing a set of words for 'For Unto Us a Child is Born', Jim wrote drawing on the St. Matthew gospel.
A PDF document is attached below. It contains the words and the notation for three fiddle parts.